In this thesis we consider the characters of the normalizer and the centralizer of Sylow tori. Hereby we take a finite group of Lie type as a fixpoint subgroup in a simply-connected simple group of a Frobenius map. For each Sylow torus S of the corresponding algebraic group we show, that every irreducible character of the centralizer of S in G extends to its inertia group in the normalizer of S. The motivation for the problem considered in this thesis arises from the study of height 0 characters of finite reductive groups in the context of the McKay-Conjecture. Due to recent results of Isaacs, Malle, and Navarro the McKay-Conjecture holds for a prime r and a group H if all non-abelian simple groups 'involved' in H are good for r. Together with the result above recent work of Malle shows that some important and necessary conditions are satisfied for the 'goodness' of simple groups of Lie type if the prime r differs from the defining characteristic. We prove explicit statements for the structure of the centralizers and normalizers of a Sylow torus, by making use of the Steinberg presentation. In addition we use the extended Weyl group, introduced by Tits, and its strong connections to braid groups. The result is proven case by case according to the underlying root system and by means of inheritance rules for extensibility of characters, also proven in this thesis.